Finite Group Databasebeta

← C4×#16810523 #27305276

Subgroups — C4×#16810523 #27305276

Order 13568.

2894 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D53C211yesmaximal, characteristic
2C2×#16810523C212yesmaximal
3C2×C4×#11719919C211yesmaximal, characteristic, complemented
4C2×C4×#11719921C211yesmaximal, characteristic, complemented
5C2×C4×#11719921C211yesmaximal, characteristic, complemented
6C2×C4×C22⋊Dic53C211yesmaximal, characteristic, complemented
7C2×C42×Dic53C211yesmaximal, characteristic, complemented
8#20272952C212yesmaximal, complemented
9#20272951C212yesmaximal, complemented
10#20272943C212yesmaximal, complemented
11C2×C4×C22⋊C4×C53C211yesmaximal, characteristic, complemented
12C23×C22⋊D53C2211yescharacteristic
13C23×C4×D53C2211yescharacteristic
14C2×C4×C22⋊D53—24no—
15C2×C4×C22⋊D53—24no—
16C2×C4×C22⋊D53C418yescomplemented
17C22×#11719919C2211yescharacteristic
18C22×#11719919C2212yes—
19C22×C22⋊Dic53C2211yescharacteristic
20C22×C22⋊Dic53C2212yes—
21C22×#11719921C2211yescharacteristic
22C22×#11719921C2212yes—
23C22×#11719921C2212yes—
24C22×C4×Dic53C2212yes—
25C22×C4×Dic53C2211yescharacteristic
26C22×C4×Dic53C2212yes—
27C22×C4×Dic53C2211yescharacteristic
28C22×C4×Dic53C2211yescharacteristic
29#16810523C4116yesdirect product factor
30C4×#11719919—24no—
31C4×#11719921—24no—
32C4×#11719921—24no—
33C4×C22⋊Dic53—24no—
34C2×#13133124C2212yes—
35C2×#13133124C2212yes—
36C2×#13133124C2212yes—
37C2×#13133124C2212yes—
38C42×Dic53—24no—
39C24×C4×C53C2211yescharacteristic
40C22×C22⋊C4×C53C2212yes—
41C22×C42×C53C2211yescharacteristic
42C22×C42×C53C2211yescharacteristic
43C4×C22⋊C4×C53—24no—
44C2×#95×C53C2212yes—
45C24×D53C2311yescharacteristic
46C22×C22⋊D53—22no—
47C22×C22⋊D53—22no—
48C22×C22⋊D53—24no—
49C22×C22⋊D53C2×C418yes—
50C22×C22⋊D53C2×C414yes—
51C23×Dic53C2312yes—
52C23×Dic53C2311yescharacteristic
53C23×Dic53C2311yescharacteristic
54C23×Dic53C2312yes—
55C23×Dic53C2311yescharacteristic
56C22×C4×D53—22no—
57C22×C4×D53—22no—
58C22×C4×D53—22no—
59C22×C4×D53—22no—
60C22×C4×D53—22no—
61C22×C4×D53—22no—
62C22×C4×D53C2×C414yes—
63C4×C22⋊D53—232no—
64C2×#11719919—22no—
65C2×#11719919—22no—
66C2×#11719919—24no—
67C2×#11719919—24no—
68C2×#11719919C2×C414yes—
69C2×#11719919C2×C418yescomplemented
70C2×C22⋊Dic53—22no—
71C2×C22⋊Dic53—22no—
72C2×C22⋊Dic53—24no—
73C2×C22⋊Dic53—24no—
74C2×C22⋊Dic53C2×C414yes—
75C2×C22⋊Dic53C2×C418yescomplemented
76C2×#11719921—24no—
77C2×#11719921—24no—
78C2×#11719921—22no—
79C2×#11719921—22no—
80C2×#11719921—24no—
81C2×#11719921—24no—
82C2×#11719921C2×C414yes—
83C2×#11719921C2×C418yescomplemented
84C2×#11719921C2×C418yescomplemented
85C2×C4×Dic53—22no—
86C2×C4×Dic53—22no—
87C2×C4×Dic53—22no—
88C2×C4×Dic53—22no—
89C2×C4×Dic53—24no—
90C2×C4×Dic53—22no—
91C2×C4×Dic53—24no—
92C2×C4×Dic53—24no—
93C2×C4×Dic53—24no—
94C2×C4×Dic53—24no—
95C2×C4×Dic53C2×C414yes—
96C2×C4×Dic53C2×C418yescomplemented
97C2×C4×Dic53D414yes—
98C2×C4×Dic53D414yes—
99C2×C4×Dic53D414yescomplemented
100#13133124—24no—
101#13133124—24no—
102#13133124—24no—
103#13133124—24no—
104C25×C53C2311yescharacteristic
105C23×C4×C53—22no—
106C23×C4×C53—22no—
107C23×C4×C53—22no—
108C23×C4×C53—22no—
109C23×C4×C53—22no—
110C23×C4×C53—22no—
111C23×C4×C53C2×C414yes—
112C23×C4×C53C2312yes—
113C23×C4×C53C2311yescharacteristic
114C23×C4×C53C2312yes—
115C23×C4×C53C2311yescharacteristic
116C2×C22⋊C4×C53—24no—
117C2×C22⋊C4×C53—24no—
118C2×C22⋊C4×C53C2×C418yescomplemented
119C2×C42×C53—22no—
120C2×C42×C53—22no—
121C2×C42×C53—22no—
122C2×C42×C53—22no—
123C2×C42×C53—22no—
124C2×C42×C53D414yescomplemented
125#95×C53—24no—
126C24×C53—21no—
127C24×C53—21no—
128C24×C53—21no—
129C24×C53—21no—
130C24×C53—22no—
131C24×C53—21no—
132C24×C53—21no—
133C24×C53—22no—
134C24×C53—22no—
135C24×C53C22×C414yes—
136C24×C53C22×C412yes—
137C24×C53C2411yescharacteristic
138C23×D53—21no—
139C23×D53—21no—
140C23×D53—21no—
141C23×D53—21no—
142C23×D53—22no—
143C23×D53—22no—
144C23×D53—21no—
145C23×D53—21no—
146C23×D53—22no—
147C23×D53C22×C412yes—
148C23×D53C22×C414yes—
149C22×C4×C53—22no—
150C22×C4×C53—22no—
151C22×C4×C53—22no—
152C22×C4×C53—22no—
153C22×C4×C53—21no—
154C22×C4×C53—22no—
155C22×C4×C53—22no—
156C22×C4×C53—22no—
157C22×C4×C53—21no—
158C22×C4×C53—21no—
159C22×C4×C53—21no—
160C22×C4×C53—22no—
161C22×C4×C53—21no—
162C22×C4×C53—21no—
163C22×C4×C53—22no—
164C22×C4×C53—22no—
165C22×C4×C53—28no—
166C22×C4×C53—28no—
167C22×C4×C53—28no—
168C22×C4×C53—44no—
169C22×C4×C53—44no—
170C22×C4×C53—44no—
171C22×C4×C53—44no—
172C22×C4×C53C22×C414yes—
173C22×C4×C53C22×C412yes—
174C22×C4×C53C22×C414yes—
175C22×C4×C53C22×C412yes—
176C22×C4×C53C2×D414yes—
177C22×C4×C53C2×D412yes—
178C22×C4×C53C2×D412yes—
179C22×C4×C53C2×D412yes—
180C22×C4×C53C2×D412yes—
181C22×C4×C53#4114yes—
182C22×C4×C53#4112yes—
183C22×C4×C53#4112yes—
184C2×C22⋊D53—28no—
185C2×C22⋊D53—28no—
186C2×C22⋊D53—216no—
187C2×C22⋊D53—216no—
188C2×C22⋊D53C42116yescomplemented
189C22×Dic53—22no—
190C22×Dic53—22no—
191C22×Dic53—22no—
192C22×Dic53—22no—
193C22×Dic53—22no—
194C22×Dic53—22no—
195C22×Dic53—21no—
196C22×Dic53—21no—
197C22×Dic53—22no—
198C22×Dic53—22no—
199C22×Dic53—22no—
200C22×Dic53—21no—
201C22×Dic53—21no—
202C22×Dic53—22no—
203C22×Dic53—22no—
204C22×Dic53—22no—
205C22×Dic53—21no—
206C22×Dic53—21no—
207C22×Dic53C22×C414yes—
208C22×Dic53C22×C412yes—
209C22×Dic53C22×C412yes—
210C22×Dic53C22×C414yes—
211C22×Dic53C22×C412yes—
212C22×Dic53C22×C414yes—
213C22×Dic53C2×D412yes—
214C22×Dic53C2×D412yes—
215C22×Dic53C2×D414yes—
216C22×Dic53C2×D412yes—
217C22×Dic53C2×D412yes—
218C22×Dic53#4114yes—
219C22×Dic53#4114yes—
220C2×C4×D53—28no—
221C2×C4×D53—28no—
222C2×C4×D53—28no—
223C2×C4×D53—44no—
224C2×C4×D53—44no—
225C2×C4×D53—44no—
226C2×C4×D53—44no—
227C22⋊C4×C53—216no—
228C42×C53—28no—
229C42×C53—44no—
230C22⋊Dic53—28no—
231C22⋊Dic53—216no—
232#11719921—216no—
233#11719921—28no—
234#11719921—216no—
235#11719919—28no—
236#11719919—216no—
237C4×Dic53—216no—
238C4×Dic53—28no—
239C4×Dic53—216no—
240C4×Dic53—44no—
241C4×Dic53C22⋊C4116yescomplemented
242C23×C53—22no—
243C23×C53—22no—
244C23×C53—24no—
245C23×C53—24no—
246C23×C53—22no—
247C23×C53—22no—
248C23×C53—24no—
249C23×C53—24no—
250C23×C53—24no—
251C23×C53—22no—
252C23×C53—22no—
253C23×C53—24no—
254C23×C53—41no—
255C23×C53—41no—
256C23×C53—42no—
257C23×C53—41no—
258C23×C53—42no—
259C23×C53—42no—
260C23×C53—41no—
261C23×C53—42no—
262C23×C53—42no—
263C23×C53—42no—
264C23×C53C2×C4214yes—
265C23×C53C23×C411yescharacteristic
266C23×C53C23×C412yes—
267C23×C53C22×D411yescharacteristic
268C23×C53C22×D411yescharacteristic
269C23×C53C22×D411yescharacteristic
270C23×C53C22×D411yescharacteristic
271C23×C53C2×#4112yes—
272C23×C53C2×#4112yes—
273C23×C53C2×#4111yescharacteristic
274C23×C53C2×#4111yescharacteristic
275C23×C53C2×#4112yes—
276C22×D53—22no—
277C22×D53—22no—
278C22×D53—22no—
279C22×D53—22no—
280C22×D53—24no—
281C22×D53—24no—
282C22×D53—24no—
283C22×D53—24no—
284C22×D53—24no—
285C22×D53—22no—
286C22×D53—22no—
287C22×D53—24no—
288C22×D53—41no—
289C22×D53—41no—
290C22×D53—42no—
291C22×D53—41no—
292C22×D53—42no—
293C22×D53—42no—
294C22×D53—41no—
295C22×D53—42no—
296C22×D53—42no—
297C22×D53—42no—
298C22×D53C2×C4214yes—
299C2×C4×C53—24no—
300C2×C4×C53—24no—
301C2×C4×C53—24no—
302C2×C4×C53—24no—
303C2×C4×C53—24no—
304C2×C4×C53—24no—
305C2×C4×C53—22no—
306C2×C4×C53—22no—
307C2×C4×C53—22no—
308C2×C4×C53—24no—
309C2×C4×C53—24no—
310C2×C4×C53—24no—
311C2×C4×C53—41no—
312C2×C4×C53—41no—
313C2×C4×C53—41no—
314C2×C4×C53—41no—
315C2×C4×C53—42no—
316C2×C4×C53—42no—
317C2×C4×C53—42no—
318C2×C4×C53—42no—
319C2×C4×C53—416no—
320C2×C4×C53C2×C22⋊C414yes—
321C2×C4×C53C4×D414yes—
322C2×C4×C53C4×D414yes—
323C2×C4×C53C4×D418yescomplemented
324C2×C4×C53#12114yes—
325C2×C4×C53#12114yes—
326C2×C4×C53#12414yes—
327C2×C4×C53#12714yes—
328C22⋊D53—232no—
329C2×Dic53—24no—
330C2×Dic53—22no—
331C2×Dic53—22no—
332C2×Dic53—24no—
333C2×Dic53—24no—
334C2×Dic53—24no—
335C2×Dic53—24no—
336C2×Dic53—24no—
337C2×Dic53—24no—
338C2×Dic53—24no—
339C2×Dic53—22no—
340C2×Dic53—22no—
341C2×Dic53—22no—
342C2×Dic53—24no—
343C2×Dic53—24no—
344C2×Dic53—24no—
345C2×Dic53—41no—
346C2×Dic53—41no—
347C2×Dic53—41no—
348C2×Dic53—41no—
349C2×Dic53—42no—
350C2×Dic53—42no—
351C2×Dic53—42no—
352C2×Dic53—42no—
353C2×Dic53C2×C4214yes—
354C2×Dic53C2×C22⋊C414yes—
355C2×Dic53C2×C22⋊C414yes—
356C2×Dic53#11714yes—
357C2×Dic53C4×D418yes—
358C2×Dic53C4×D418yes—
359C2×Dic53C4×D418yescomplemented
360C4×D53—416no—
361C4×#390—531nomaximal, Sylow
362C22×C53—24no—
363C22×C53—24no—
364C22×C53—24no—
365C22×C53—44no—
366C22×C53—42no—
367C22×C53—42no—
368C22×C53—42no—
369C22×C53—42no—
370C22×C53—44no—
371C22×C53—44no—
372C22×C53—44no—
373C22×C53C22×C4211yescharacteristic
374C22×C53C22×C22⋊C411yescharacteristic
375C22×C53C2×#11711yescharacteristic
376C22×C53C2×C4×D412yes—
377C22×C53C2×C4×D412yes—
378C22×C53C2×C4×D412yes—
379C22×C53C2×C4×D411yescharacteristic
380C22×C53C2×C4×D412yes—
381C22×C53C2×C4×D411yescharacteristic
382C22×C53C4×#4112yes—
383C22×C53C4×#4111yescharacteristic
384C22×C53C4×#4111yescharacteristic
385C22×C53C4×#4112yes—
386C22×C53C2×#12111yescharacteristic
387C22×C53C2×#12111yescharacteristic
388C22×C53#52512yes—
389C22×C53C2×#12411yescharacteristic
390C22×C53#52912yes—
391C22×C53#52912yes—
392C22×C53C2×#12711yescharacteristic
393C22×C53#53212yes—
394C22×C53#53212yes—
395C22×C53#53212yes—
396C2×D53—24no—
397C2×D53—24no—
398C2×D53—24no—
399C2×D53—44no—
400C2×D53—42no—
401C2×D53—42no—
402C2×D53—42no—
403C2×D53—42no—
404C2×D53—44no—
405C2×D53—44no—
406C2×D53—44no—
407C4×C53—28no—
408C4×C53—44no—
409C4×C53—42no—
410C4×C53#39018yescomplemented
411Dic53—24no—
412Dic53—28no—
413Dic53—44no—
414Dic53—42no—
415Dic53C4×C22⋊C418yescomplemented
416C22×C4×D4—531no—
417C2×#390—532no—
418C2×C4×C4⋊C4—531no—
419C2×C4×C22⋊C4—531no—
420C2×C4×C22⋊C4—531no—
421C2×C4×C22⋊C4—531no—
422C2×C4×C22⋊C4D5311yescharacteristic, complemented
423C2×C43—531no—
424#1437—532no—
425#1437—532no—
426C4⋊#95—532no—
427C2×C53—44no—
428C2×C53C2×C4×C22⋊C411yescharacteristic
429C2×C53C42×D411yescharacteristic
430C2×C53C42×D411yescharacteristic
431C2×C53C2×#39011yescharacteristic
432C2×C53#229311yescharacteristic
433C2×C53#229311yescharacteristic
434C2×C53#229711yescharacteristic
435C2×C53C4×#12112yes—
436C2×C53C4×#12112yes—
437C2×C53C4×#12412yes—
438C2×C53C4×#12712yes—
439D53—44no—
440C23×D4—531no—
441C24×C4—531no—
442C24×C4C2×D5311yescharacteristic
443C2×C4×D4—538no—
444C2×C4×D4—1064no—
445C2×C4×D4—1064no—
446C22×C4⋊C4—531no—
447C22×C4⋊C4—532no—
448C22×C22⋊C4—531no—
449C22×C22⋊C4—532no—
450C22×C22⋊C4—531no—
451C22×C22⋊C4—532no—
452C22×C22⋊C4—532no—
453C22×C22⋊C4C2×D5312yes—
454C22×C42—531no—
455C22×C42—532no—
456C22×C42—531no—
457C22×C42—532no—
458C22×C42—531no—
459C22×C42C2×D5311yescharacteristic
460C22×C42C2×D5311yescharacteristic
461#390—5316no—
462C4×C4⋊C4—1064no—
463C4×C22⋊C4—24no—
464C4×C22⋊C4—1064no—
465C4×C22⋊C4—1064no—
466C4×C22⋊C4—1064no—
467C2×#95—532no—
468C2×#95—532no—
469C2×#95—532no—
470C2×#95—532no—
471C2×#95C2×D5312yes—
472C43—1064no—
473C53C4×#39011yescharacteristic, complemented, Sylow
474C25—531no—
475C25C22×D5311yescharacteristic
476C22×D4—534no—
477C22×D4—538no—
478C22×D4—1062no—
479C22×D4—1062no—
480C22×D4—1064no—
481C23×C4—22no—
482C23×C4—22no—
483C23×C4—22no—
484C23×C4—22no—
485C23×C4—22no—
486C23×C4—22no—
487C23×C4—531no—
488C23×C4—531no—
489C23×C4—532no—
490C23×C4—532no—
491C23×C4—531no—
492C23×C4—534no—
493C23×C4—1062no—
494C23×C4—1062no—
495C23×C4—1062no—
496C23×C4—1062no—
497C23×C4—1062no—
498C23×C4—1062no—
499C23×C4C4×D5314yes—
500C23×C4C22×D5312yes—
501C23×C4C22×D5311yescharacteristic
502C23×C4C22×D5312yes—
503C23×C4C22×D5311yescharacteristic
504C4×D4—10632no—
505C2×C4⋊C4—534no—
506C2×C4⋊C4—538no—
507C2×C4⋊C4—1062no—
508C2×C4⋊C4—1062no—
509C2×C4⋊C4—1064no—
510C2×C4⋊C4—1064no—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—24no—
513C2×C22⋊C4—534no—
514C2×C22⋊C4—538no—
515C2×C22⋊C4—534no—
516C2×C22⋊C4—538no—
517C2×C22⋊C4—538no—
518C2×C22⋊C4—1062no—
519C2×C22⋊C4—1062no—
520C2×C22⋊C4—1064no—
521C2×C22⋊C4—1064no—
522C2×C22⋊C4—1062no—
523C2×C22⋊C4—1062no—
524C2×C22⋊C4—1064no—
525C2×C22⋊C4—1064no—
526C2×C22⋊C4—1064no—
527C2×C22⋊C4—1064no—
528C2×C22⋊C4C4×D5318yescomplemented
529C2×C42—22no—
530C2×C42—22no—
531C2×C42—22no—
532C2×C42—22no—
533C2×C42—22no—
534C2×C42—534no—
535C2×C42—534no—
536C2×C42—534no—
537C2×C42—538no—
538C2×C42—534no—
539C2×C42—1064no—
540C2×C42—1064no—
541C2×C42—1064no—
542C2×C42—1064no—
543C2×C42—1064no—
544C2×C42—1062no—
545C2×C42—1062no—
546C2×C42—1062no—
547C2×C42—1062no—
548C2×C42—1062no—
549C2×C42C22⋊D5314yescomplemented
550#95—24no—
551#95—1064no—
552#95—1064no—
553#95—1064no—
554#95—1064no—
555C24—21no—
556C24—21no—
557C24—21no—
558C24—21no—
559C24—22no—
560C24—22no—
561C24—21no—
562C24—22no—
563C24—21no—
564C24—534no—
565C24—532no—
566C24—1061no—
567C24—1061no—
568C24—1061no—
569C24—1061no—
570C24—1062no—
571C24—1062no—
572C24—1061no—
573C24—1062no—
574C24—1061no—
575C24C2×C4×D5314yes—
576C24C2×C4×D5312yes—
577C24C23×D5311yescharacteristic
578C2×D4—5316no—
579C2×D4—1068no—
580C2×D4—1068no—
581C2×D4—10616no—
582C2×D4—10616no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—21no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—21no—
597C22×C4—22no—
598C22×C4—21no—
599C22×C4—28no—
600C22×C4—28no—
601C22×C4—28no—
602C22×C4—44no—
603C22×C4—44no—
604C22×C4—44no—
605C22×C4—44no—
606C22×C4—532no—
607C22×C4—534no—
608C22×C4—532no—
609C22×C4—532no—
610C22×C4—534no—
611C22×C4—532no—
612C22×C4—534no—
613C22×C4—532no—
614C22×C4—534no—
615C22×C4—532no—
616C22×C4—534no—
617C22×C4—534no—
618C22×C4—532no—
619C22×C4—1062no—
620C22×C4—1062no—
621C22×C4—1062no—
622C22×C4—1062no—
623C22×C4—1062no—
624C22×C4—1062no—
625C22×C4—1061no—
626C22×C4—1062no—
627C22×C4—1062no—
628C22×C4—1061no—
629C22×C4—1061no—
630C22×C4—1061no—
631C22×C4—1062no—
632C22×C4—1062no—
633C22×C4—1062no—
634C22×C4—1061no—
635C22×C4—1062no—
636C22×C4—1061no—
637C22×C4—1068no—
638C22×C4—1068no—
639C22×C4—1068no—
640C22×C4—2124no—
641C22×C4—2124no—
642C22×C4—2124no—
643C22×C4—2124no—
644C22×C4C2×C4×D5314yes—
645C22×C4C2×C4×D5312yes—
646C22×C4C2×C4×D5314yes—
647C22×C4C2×C4×D5312yes—
648C22×C4#1171994514yes—
649C22×C4#1171994512yes—
650C22×C4D4×D5312yes—
651C22×C4D4×D5312yes—
652C22×C4D4×D5312yes—
653C22×C4#1171994712yes—
654C22×C4C2×C22⋊D5314yes—
655C22×C4C2×C22⋊D5312yes—
656C4⋊C4—1068no—
657C4⋊C4—10616no—
658C22⋊C4—216no—
659C22⋊C4—1068no—
660C22⋊C4—10616no—
661C22⋊C4—1068no—
662C22⋊C4—10616no—
663C22⋊C4—10616no—
664C42—28no—
665C42—44no—
666C42—5316no—
667C42—10616no—
668C42—10616no—
669C42—1068no—
670C42—2124no—
671C23—22no—
672C23—22no—
673C23—24no—
674C23—24no—
675C23—24no—
676C23—22no—
677C23—24no—
678C23—22no—
679C23—24no—
680C23—22no—
681C23—24no—
682C23—22no—
683C23—41no—
684C23—41no—
685C23—42no—
686C23—41no—
687C23—42no—
688C23—42no—
689C23—41no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—534no—
694C23—1062no—
695C23—1062no—
696C23—1064no—
697C23—1064no—
698C23—1064no—
699C23—1062no—
700C23—1064no—
701C23—1062no—
702C23—1064no—
703C23—1062no—
704C23—1064no—
705C23—1062no—
706C23—2121no—
707C23—2121no—
708C23—2122no—
709C23—2121no—
710C23—2122no—
711C23—2122no—
712C23—2121no—
713C23—2122no—
714C23—2122no—
715C23—2122no—
716C23C42×D5314yes—
717C23C22×C4×D5311yescharacteristic
718C23C22×C4×D5312yes—
719C23C2×D4×D5311yescharacteristic
720C23C2×D4×D5311yescharacteristic
721C23C2×D4×D5311yescharacteristic
722C23C22×C22⋊D5311yescharacteristic
723C23#41×D5312yes—
724C23#41×D5312yes—
725C23C2×#1171994711yescharacteristic
726C23C2×#1171994511yescharacteristic
727C23C2×#1171994512yes—
728D4—10632no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—22no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—22no—
739C2×C4—24no—
740C2×C4—22no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—42no—
745C2×C4—41no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—416no—
750C2×C4—534no—
751C2×C4—534no—
752C2×C4—534no—
753C2×C4—538no—
754C2×C4—538no—
755C2×C4—534no—
756C2×C4—538no—
757C2×C4—1064no—
758C2×C4—1062no—
759C2×C4—1062no—
760C2×C4—1064no—
761C2×C4—1064no—
762C2×C4—1064no—
763C2×C4—1064no—
764C2×C4—1064no—
765C2×C4—1064no—
766C2×C4—1064no—
767C2×C4—1062no—
768C2×C4—1064no—
769C2×C4—1064no—
770C2×C4—1062no—
771C2×C4—1064no—
772C2×C4—1062no—
773C2×C4—2121no—
774C2×C4—2121no—
775C2×C4—2121no—
776C2×C4—2122no—
777C2×C4—2121no—
778C2×C4—2122no—
779C2×C4—2122no—
780C2×C4—2122no—
781C2×C4—21216no—
782C2×C4C22⋊C4×D5314yes—
783C2×C4#1313317714yes—
784C2×C4C4×C22⋊D5314yes—
785C2×C4C4×C22⋊D5318yescomplemented
786C2×C4#1313318914yes—
787C2×C4#1313319014yes—
788C2×C4#1313320314yes—
789C2×C4#1313321314yes—
790C22—24no—
791C22—24no—
792C22—24no—
793C22—44no—
794C22—44no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—44no—
800C22—44no—
801C22—1064no—
802C22—1064no—
803C22—1064no—
804C22—2124no—
805C22—2124no—
806C22—2122no—
807C22—2122no—
808C22—2122no—
809C22—2122no—
810C22—2124no—
811C22—2124no—
812C22C2×C42×D5311yescharacteristic
813C22C2×C22⋊C4×D5311yescharacteristic
814C22#117×D5311yescharacteristic
815C22C4×D4×D5312yes—
816C22C4×D4×D5312yes—
817C22C4×D4×D5312yes—
818C22C2×#1313317711yescharacteristic
819C22C2×C4×C22⋊D5312yes—
820C22C2×C4×C22⋊D5311yescharacteristic
821C22C4×#1171994712yes—
822C22#1681109111yescharacteristic
823C22C4×#1171994512yes—
824C22C4×#1171994511yescharacteristic
825C22C2×#1313318911yescharacteristic
826C22C2×#1313319011yescharacteristic
827C22#1681113212yes—
828C22C2×#1313320311yescharacteristic
829C22#1681115112yes—
830C22#1681115312yes—
831C22C2×#1313321311yescharacteristic
832C22#1681116912yes—
833C22#1681117012yes—
834C22#1681117012yes—
835C4—28no—
836C4—44no—
837C4—42no—
838C4—538no—
839C4—1064no—
840C4—1068no—
841C4—2124no—
842C4—2122no—
843C4#1681052318yesdirect product factor
844C2—44no—
845C2—2124no—
846C2C4×C22⋊C4×D5311yescharacteristic
847C2C4×#1313317711yescharacteristic
848C2C42×C22⋊D5311yescharacteristic
849C2C2×#1681052311yescharacteristic
850C2#2027717411yescharacteristic
851C2#2027717811yescharacteristic
852C2#2027720111yescharacteristic
853C2C4×#1313318912yes—
854C2C4×#1313319012yes—
855C2C4×#1313320312yes—
856C2C4×#1313321312yes—
subgroupG/H
centerC23×C4C22×D53
commutatorC22×C53C22×C42
FrattiniC24C23×D53
FittingC2×C4×C22⋊C4×C53C2
socle, cosocleC24×C53C24
prime radicalC23×C22⋊D53C22
hypercenterC2×C4×C22⋊C4D53
hypocenterC53C4×#390
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C23×C4 ◁ C2×C4×C22⋊C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. C2×C4×#11719919C2semidirect
4. C2×C4×#11719921C2semidirect
5. C2×C4×#11719921C2semidirect
6. C2×C4×C22⋊Dic53C2semidirect
7. C2×C42×Dic53C2semidirect
8. #20272952C2semidirect
9. #20272951C2semidirect
10. #20272943C2semidirect
11. C2×C4×C22⋊C4×C53C2semidirect
16. C2×C4×C22⋊D53C4semidirect
29. #16810523C4direct (N × H)
69. C2×#11719919C2×C4semidirect
75. C2×C22⋊Dic53C2×C4semidirect
83. C2×#11719921C2×C4semidirect
84. C2×#11719921C2×C4semidirect
96. C2×C4×Dic53C2×C4semidirect
99. C2×C4×Dic53D4semidirect
118. C2×C22⋊C4×C53C2×C4semidirect
124. C2×C42×C53D4semidirect
188. C2×C22⋊D53C42semidirect
241. C4×Dic53C22⋊C4semidirect
323. C2×C4×C53C4×D4semidirect
359. C2×Dic53C4×D4semidirect
410. C4×C53#390semidirect
415. Dic53C4×C22⋊C4semidirect
422. C2×C4×C22⋊C4D53semidirect
473. C53C4×#390semidirect
528. C2×C22⋊C4C4×D53semidirect
549. C2×C42C22⋊D53semidirect
785. C2×C4C4×C22⋊D53semidirect
843. C4#16810523direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×C4×C22⋊D532
C2×#168105232
C2×C4×#117199192
C2×C4×#117199212
C2×C4×C22⋊Dic532
C2×C42×Dic532
#202729522
#202729512
#202729432
C2×C4×C22⋊C4×C532
C4×#39053